Problem: Solve for $x$ and $y$ using elimination. ${3x+6y = 39}$ ${-3x+5y = 5}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $11y = 44$ $\dfrac{11y}{{11}} = \dfrac{44}{{11}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {3x+6y = 39}\thinspace$ to find $x$ ${3x + 6}{(4)}{= 39}$ $3x+24 = 39$ $3x+24{-24} = 39{-24}$ $3x = 15$ $\dfrac{3x}{{3}} = \dfrac{15}{{3}}$ ${x = 5}$ You can also plug ${y = 4}$ into $\thinspace {-3x+5y = 5}\thinspace$ and get the same answer for $x$ : ${-3x + 5}{(4)}{= 5}$ ${x = 5}$